The count of a local position is the net amount of territory we calculate for it. When the position has been played out and the count is definite, we just call it the score.
Count is like the expected score or average, but it is a stronger concept. If there are no kos (either now or later), and the overall count is in your favor, and you have sente, you will win with correct play. You can't say that for averages or expected scores.
Conventionally, the count or score for Black is positive, for White, negative.
See Method of Multiples for one way of determining count and further explanation.